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AN ALGEBRA WHOSE SUBALGEBRAS ARE CHARACTERIZED BY DENSITY

Published online by Cambridge University Press:  22 July 2015

ALESSANDRO VIGNATI
ALESSANDRO VIGNATI*
Affiliation:
YORK UNIVERSITY DEPARTMENT OF MATHEMATICS AND STATISTICS 4700 KEELE ST., TORONTO ONTARIO, M3J 1P3, CANADAE-mail: ale.vignati@gmail.com
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Abstract

We refine a construction of Choi, Farah, and Ozawa to build a nonseparable amenable operator algebra ${\rm {\cal A}}$ ⊆ ℓ∞ (M2) whose nonseparable subalgebras, including ${\rm {\cal A}}$, are not isomorphic to a C*-algebra. This is done using a Luzin gap and a uniformly bounded group representation.

Next, we study additional properties of ${\rm {\cal A}}$ and of its separable subalgebras, related to the Kadison Kastler metric.

Keywords

46L0547L40amenable Banach algebraLuzin gapnonseparable algebrasunitarizable group representation
Type
Articles
Information
The Journal of Symbolic Logic , Volume 80 , Issue 3 , September 2015 , pp. 1066 - 1074
Copyright
Copyright © The Association for Symbolic Logic 2015 

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References

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